The general local-search paradigm is simple: starting with any candidate solution to a problem, repeatedly look for small alterations that can possibly lead to a better solution.
The idea dates back to work on the TSP, starting with the 2-opt heuristic by [1]}.
In Flood's algorithm, the small alteration consists of removing two edges in a TSP tour (considering a tour as a circuit in a graph) and reconnecting the resulting paths into a new tour, by adding two other edges.
This was quickly extended to 3-opt, removing and adding 3 edges at a time, by [2]} and [3]}, and later to a variable \(k\) -opt algorithm by [4]}.
